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A301647
a(n) = n^3 - (n mod 2).
0
0, 8, 26, 64, 124, 216, 342, 512, 728, 1000, 1330, 1728, 2196, 2744, 3374, 4096, 4912, 5832, 6858, 8000, 9260, 10648, 12166, 13824, 15624, 17576, 19682, 21952, 24388, 27000, 29790, 32768, 35936, 39304, 42874, 46656, 50652, 54872, 59318, 64000, 68920, 74088, 79506, 85184, 91124
OFFSET
1,2
COMMENTS
a(n) is the circumference of the n X n X n grid graph for n > 1.
LINKS
Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Grid Graph
FORMULA
a(n) = (2 n^3 + (-1)^n - 1)/2.
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
G.f.: 2*x^2*(4 + x + x^2)/((-1 + x)^4*(1 + x)).
MAPLE
seq(n^3-modp(n, 2), n=1..50); # Muniru A Asiru, Mar 25 2018
MATHEMATICA
Table[n^3 - Mod[n, 2], {n, 20}]
Table[(2 n^3 + (-1)^n - 1)/2, {n, 20}]
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 8, 26, 64, 124}, 20]
CoefficientList[Series[2 x (4 + x + x^2)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]
PROG
(GAP) List([1..50], n->n^3- n mod 2); # Muniru A Asiru, Mar 25 2018
(PARI) a(n) = n^3 - (n%2); \\ Altug Alkan, Mar 25 2018
CROSSREFS
Cf. A137932 (circumference of n X n grid graph).
Sequence in context: A002901 A350163 A213769 * A050471 A088024 A296112
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 25 2018
STATUS
approved